March 9, 2016

From the comments received over my last article on Randomness in Stock Prices, there appears to be some confusion for some in the terms used. I'll try to clarify my point of view.

Usually, the word random implies that you cannot predict the next move better than by chance, otherwise it would not be random. You can assign odds and probabilities to the outcome from observed statistics. For instance, in a random game like heads or tails, you can assign 0.50 as the probability of getting head on the next flip of a coin.

If your bet was right, meaning you won, you wouldn't be able to attribute the outcome to any kind of skills you might think you have, prescient, educated, or otherwise. You simply would have won by chance alone.

You can guess, you can make a bet, but you can't put any guarantee to it, only, at most, probabilities, and this only if the game has been totally defined, like in a heads or tails game. Meaning that the odds of any outcome are known in advance. Which is not the case for stock price variations.

Stock price variations are not preset values or fixed amounts. They can fluctuate tremendously from one day to the next. You literally don't know if IBM will go up or down tomorrow, be it by 5¢, \$5, or whatever. If you knew this, there would be a free lunch. You can always say: I knew it, but in reality, you did not. You just made a guess.

You can know the statistics for all the hockey games for the last century, and yet, you can't put reliable odds on the outcome for the season or for the next game. You just make a bet and live with it, that you win or lose. Those making short-term "predictions" are just guessing on a probable outcome when, in fact, one of the two teams will have to win the game.

Using the words: random walk implies a Gaussian distribution close to a heads or tails kind of game. I hope everyone here can accept that the most expected outcome of such a game is zero. If you flip a coin a million times, will it end with a zero gain? Most probably not. Only a small percentage of all the trials will end up with zero (the most expected outcome). So, technically, your most probable outcome would be something other than zero, + or – whatever, but within the confines of 3 standard deviations on the million tosses (this is for 99.7% of all the trials). Can the few trials (0.3%) exceeding the 3 standard deviations be considered non-random walk?

Something random-like may not be a copy of a random walk or a clone of a Gaussian distribution. I prefer a Paretian distribution when viewing stock prices. It has a lot of randomness in it and is still viewed with its next outcome as almost unpredictable. The distribution could be skewed and biased up or down depending on the stock being studied. Each stock has its own signature.

We often use a stochastic equation to model price movements: dp = µdt + σdW, where the Wiener process is scaled by volatility. But this models price movements as Gaussian with a linear deterministic part and a random component which by nature is classified as unpredictable. It represents the error term of a simple linear regression. As such, have for expected value: E[σdW] = 0, or at least something tending to zero: E[σdW] → 0.

When you look closer, you see that µ and σ are themselves random-like in nature with a lot of unpredictability as well. I would say that technically, you are navigating in a tumultuous ocean of variance where the probabilities are ill-defined and changing all the time.

Something random-like may have a different distribution than a random walk. From stock price movement observations, a random-like distribution will have to contend with fat tails, outliers, gaps, black swans, and stock extinction events such as bankruptcies and frauds. Stuff that should not happen in several hundred million years suddenly appears on price charts (like the 2010 flash crash). How many predicted that? A major part of a stock price series can still be classified as quasi-random-like since short-term predictability may, at times, be quite low.

Better questions might be: How much randomness is there really? How much predictability is there in stock price series? What type of randomness are we looking at? What are the odds of the next price move? And if you ask the last question, the answer should be provable, giving a demonstration of the math leading to such odds. Giving odds out of the blue does not count as a forward probability. I can always make any bet, but it does not make it a prediction with assessable odds.

A single bet for a day on the direction of price movement is not enough to build a long-term portfolio. It is not a bet here and there that you win that really matters. It is the end game. What will your portfolio's ending value be in 20+ years? Your single-day bet requires another 5,000+ more similar trades to reach its goal. And there, you will find that your short-term "predictions" were, at best, guesses, and you will start to express them using hit rates, with average profit and loss per trade.

If you have a predictability rating of 60%, saying that you guessed right in 60% of the trades, bravo. All you have to do is continue to trade as much as you possibly can using your advantage. But, if, due to your small bet size or an insufficient number of trades, you did not perform better than the Buy & Hold with your strategy over a 20+ year period, then surprise, your methods are not worth much since anybody could have done better just sitting on their hands.

You might want to take a second look at my recent 20-year stock trading experiment. From a rather bland strategy, I transformed it into something more productive, not by using short-term predictions, but by designing long-term deterministic trading procedures. It is a 5 part series which was chronicled almost live. A more elaborate account of the undertaking can be found on my site, see stock trading strategy experiment, parts: IIIIIIIVV.

For those who say that stock prices have no randomness (since they do state that stock prices are not random), the burden of proof might be in your hands. Show the degree of predictability, show that the next 1,000 short-term bets will be with say a 90+% hit rate with a 95% confidence level. And if you can do this, can I say what a bright future you will have. I would be interested in anything you say about how you do it, but I would request numbers, not just opinions.

What I want to see is someone offering guarantees on their predictions. Not just an opinion that IBM will be up 5% tomorrow, but an assurance that their prediction will indeed occur and that they stand ready to pay the price, out of their pocket, if it does not realize. What you will see is that all these "predictioners" will abstain to guarantee their supposedly accurate and non-random based "predictions".